Stepped-frequency continuous-wave ground-penetrating radars (SFCW GPRs) are characterized
by relatively low data acquisition speed caused by stepwise slow scanning of the frequency
spectrum. The improvement of the imaging speed in SFCW GPR mostly relies on reducing
the data acquisition time. In this thesis, a paradigm of compressive sensing (CS) is explored
in order to minimize the acquisition time in three dimensional SFCW GPRs by reducing the
amount of real-time acquired data below the Nyquist rate by the use of the likely spatial sparsity
of the underground. This work analyzes the reconstructions provided by different convex and
greedy sparse recovery algorithms. Specifically, Basis Pursuit (BP), Matching Pursuit (MP),
Orthogonal Matching Pursuit (OMP), Compressive Sampling Matching Pursuit (CoSaMP),
Generalized Orthogonal Matching Pursuit (GOMP), Backtracking Iterative Hard Thresholding
(BIHT) and Regularized Orthogonal Matching Pursuit (ROMP). Data sets with synthetic underground mines are accurately reconstructed for compression ratios up to 85% causing that
the data acquisition time is reduced 6.67 times. In addition, the results show that for the data
sets of synthetic mines degraded by uniform noise, the proposed software compressive SFCW
GPR system implemented in MATLAB can be used for effective noise-removal filtering. Finally,
a real data set obtained in a bridge survey is precisely recovered for compression ratios up to 40%.